Systems and methods to improve management and monitoring of cardiovascular disease

ABSTRACT

The present invention is directed to systems and methods for identifying a cardiovascular disease of a patient. In one embodiment, the method includes obtaining measurements for a diastolic pressure, a systolic pressure, a heartbeat period, a stroke volume, and an ejection period for the patient, and then determining an aortic compliance for the patient based on these measurements. The diastolic pressure, systolic pressure, and heartbeat period are each measured directly from the patient, and the stroke volume and ejection period are each measured from echocardiogram data. In another embodiment, the method includes obtaining measurements for a diastolic pressure and a systolic pressure for the patient, obtaining an estimate of a stroke volume for the patient, and then determining an aortic compliance for the patient based on the diastolic pressure, the systolic pressure, and the stroke volume. These methods may be implemented using a computing device that optionally accesses an electronic medical record to retrieve the relevant parameters.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based on and claims priority to U.S. ProvisionalApplication Ser. No. 62/931,826 filed on Nov. 7, 2019, which isincorporated herein by reference in its entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable.

STATEMENT REGARDING JOINT RESEARCH AGREEMENT

Not applicable.

BACKGROUND OF THE INVENTION

Cardiovascular compliance, which is also referred to as capacitance, isknown to be an independent predictor for future cardiovascular events(e.g., coronary heart disease, myocardial infarction, stroke events, andtarget organ damage) regardless of previous cardiovascular diseases,age, or diabetes. A cardiovascular system with a high capacitance issaid to be compliant and soft, while a cardiovascular system with a lowcapacitance is said to be non-compliant, hard and stiff. Patients with alower-than-normal cardiovascular compliance are at risk for developingcardiovascular disease and, thus, knowledge of compliance is important.

A crude approximation for total cardiovascular compliance has been usedin the past by taking the ratio of the stroke volume of the leftventricle and the pulse pressure within the aorta. However, this methodrequires a noninvasive estimate of the stroke volume and pulse pressure,and has not been shown to be a significant or independent predictor formortality. More local measurements of arterial compliance have beenassessed using ultrasound methods or magnetic resonance imaging formeasuring the deformation of arteries while they undergo pressurepulsations from the heart. However, these methods are time consuming,and have shown their value to be primarily related to pathophysiology,pharmacology, and therapeutics, rather than for epidemiological studies.

The current “gold standard” for assessing arterial compliance has beenthe use of the carotid-femoral Pulse Wave Velocity (PMV) test. The PWVis determined by simultaneously recording the pressure waveform at twodifferent sites in the arterial tree, namely, the carotid artery in theneck and the femoral artery near the groin. These measurements aretypically taken using noninvasive methods of transcutaneous tonometry.The distance between the two arterial segments is then divided by thetime delay between the two waveforms. This calculated velocity is calledthe PWV and is intended to be an indirect measure of the regionalcompliance between the carotid and femoral arteries within the arterialtree. While the total arterial compliance of the body is of mostrelevance for assessing health, a measure of the regional compliancebetween the carotid and femoral arteries is believed to be a goodindicator of the total compliance insofar as the compliance of theselarger blood vessels tends to dominate the total compliance of the body.It has been deemed that a healthy PWV test is one that produces a resultof 6 meters/second to 7 meters/second. A PWV that exceeds 13meters/second is considered to be a strong predictor of cardiovascularmortality.

As noted above, the PWV is not a direct measure of total cardiovascularcompliance, i.e., the units of velocity (length over time) are not thesame as the units of compliance/capacitance (volume over pressure). Withthat said, it is possible to develop an equation using water hammeranalysis which shows that the compliance of the fluid conduit isinversely proportional to the square of the PWV and that the complianceincreases slightly with mean pressure. The compliance is also directlyproportional to the volume of blood in the conduit and so this too mustbe known with some degree of certainty if the PWV is to be a reasonablesurrogate for aortic compliance. Another complicating factor in usingthe PWV is that the distance between the carotid and femoral arteries isnot easy to determine, especially for men with abdominal obesity orwomen who have a large bust size. Another concern with the PMV test isthat it is not a routine measurement that is taken in the clinic orhospital for assessing cardiovascular health. Rather, it is aspecialized test that remains primarily within the realm ofcardiovascular research.

Thus, there is a need for improved systems and method for assessingaortic compliance in order to improve the management and monitoring ofpatients with cardiovascular disease.

BRIEF SUMMARY OF THE INVENTION

The present invention is directed to systems and method for assessingaortic compliance in order to improve the management and monitoring ofpatients with cardiovascular disease.

In one embodiment, a mathematical model for the compliance of the aortais derived based upon the conservation of mass, which enables aorticcompliance to be determined based on five parameters—diastolic pressure,systolic pressure, heartbeat period, stroke volume of the leftventricle, and ejection period. Blood pressure is routinely measured inthe clinic to determine the systolic and diastolic pressures of theblood-pressure pulse. The heartbeat period (i.e., heart rate) is alsoroutinely measured in the clinic. The stroke volume and ejection periodmay be determined from echocardiogram data in order to obtain accuratenumbers for a specific patient. Notably, an echocardiogram is morecommon than a PWV test. The total peripheral resistance may also bedetermined based on these same five parameters. The aortic complianceand total peripheral resistance are the lumped parameters that describethe ability of the blood vessels to absorb blood pulsations, and toresist the blood flowing from the high-pressure aorta to thelow-pressure vena cava.

The above-described method may be modified based on the assumption thatthe ejection period is equal to one-third of the heartbeat period. Inthis case, the aortic compliance and total peripheral resistance aredetermined based on the diastolic pressure, systolic pressure, heartbeatperiod, and an estimated stroke volume (it is not necessary to obtainthe ejection period from an echocardiogram). The stroke volume may beestimated, for example, based on a person's age, height, medicalhistory, weight, and/or previous measurements.

In yet another embodiment, the compliance of the aorta is determinedbased on the PWV and the mean arterial pressure. The PWV may be measuredusing known methods for obtaining the carotid-femoral PWV measurement.The mean arterial pressure may be determined based on fourparameters—diastolic pressure, systolic pressure, heartbeat period, andejection period (which may be obtained in the same manner as describedabove). The method of obtaining the mean arterial pressure may bemodified based on the assumption that the ejection period is equal toone-third of the heartbeat period, in which case only the diastolic andsystolic pressures are required.

Each of the above methods may be implemented using a computing devicethat receives the relevant parameters and/or test results (which willvary depending on which method is used), determines the aorticcompliance and/or peripheral resistance based on this information, andthen presents the aortic compliance and/or peripheral resistance via auser interface to enable a physician or other clinician to identify acardiovascular disease of the patient. In some embodiments, thecomputing device accesses an electronic medical record to retrieve therelevant parameters and/or test results.

Various other embodiments and features of the present invention aredescribed in detail below, or will be apparent to one skilled in the artbased on the disclosure provided herein, or may be learned from thepractice of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic for a section of the abdominal aorta that is usedto conduct a blood pressure analysis in accordance with one embodimentof the invention.

FIG. 2 is a schematic for an infinitesimal control volume within asegment of an aorta that is used to conduct a pulse-wave velocity (PWV)analysis in accordance with an embodiment of the invention.

FIG. 3 is a schematic for an experimental setup used to perform in vitroexperiments in relation to the blood pressure and PWV embodiments of theinvention.

FIG. 4 is a plot showing the compliance and PWV results versus the meanarterial pressure for an elastic tube.

FIG. 5 is a plot showing the compliance and PWV results versus the meanarterial pressure for a Holstein aorta.

FIG. 6 is a block diagram of a computer system that may be used toimplement the methods for determining aortic compliance and/orperipheral resistance in accordance with various embodiments of theinvention.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENT

The present invention is directed to systems and method for assessingaortic compliance in order to improve the management and monitoring ofpatients with cardiovascular disease. While the invention will bedescribed in detail below with reference to various exemplaryembodiments, it should be understood that the invention is not limitedto the specific systems or methodologies of these embodiments. Inaddition, although the exemplary embodiments are described as embodyingseveral different inventive features, one skilled in the art willappreciate that any one of these features could be implemented withoutthe others in accordance with the invention.

In the present disclosure, references to “one embodiment,” “anembodiment,” “an exemplary embodiment,” or “embodiments” mean that thefeature or features being described are included in at least oneembodiment of the invention. Separate references to “one embodiment,”“an embodiment,” “an exemplary embodiment,” or “embodiments” in thisdisclosure do not necessarily refer to the same embodiment and are alsonot mutually exclusive unless so stated and/or except as will be readilyapparent to one skilled in the art from the description. For example, afeature, function, etc. described in one embodiment may also be includedin other embodiments, but is not necessarily included. Thus, the presentinvention can include a variety of combinations and/or integrations ofthe embodiments described herein.

Generally, the present disclosure describes two different embodimentsfor assessing aortic compliance: (1) a blood pressure embodiment inwhich the aortic compliance is based on five parameters (i.e., strokevolume ΔV, ejection period T_(e), heartbeat period T, diastolic pressureP_(d), and systolic pressure P_(s)) and (2) a PWV embodiment in whichthe aortic compliance is based on the PWV and the mean arterial pressureP_(m). These two embodiments have both been shown to be effective inassessing aortic compliance through in vitro experimentation and, assuch, either embodiment may be used depending upon the available data.Provided below is a description of the blood pressure and PWVembodiments, experimentation data for each of these embodiments, and acomputing system that may be used to implement these embodiments in aclinical setting.

The disclosure of the blood pressure and PWV embodiments provided belowincludes numerous symbols that are used to reference certainterms/variables, as shown in Table 1 below:

TABLE 1 Symbol Term/Variable a Area A local cross-sectional area of theaorta Ā average cross-sectional area of the aorta A₀ localcross-sectional area of the aorta when the pressure is zero c wavepropagation speed C total aortic compliance D outside diameter of theaorta D₀ outside diameter of the aorta when the blood pressure is zero dinside diameter of the aorta d₀ inside diameter of the aorta when theblood pressure is zero E modulus of elasticity L length of the aortan{circumflex over ( )} unit vector pointing outwardly normal from thecontrol surface p fluid momentum vector in the positive x-direction Pinstantaneous blood pressure P_(d) diastolic pressure P_(m) meanarterial pressure P_(s) systolic pressure P_(1,2) pressures at the twoends of the aorta PWV pulse wave velocity Q volumetric flow rate fromthe left ventricle into the aorta q_(a) volumetric flow rate across theaortic valve q_(m) volumetric flow rate across the mitral valve R totalperipheral resistance R² statistical coefficient-of-determination t timeT heartbeat period T_(e) ejection period of the left ventricle duringsystole u fluid-velocity vector in the positive x-direction u bloodvelocity within the aorta ū average fluid velocity within the controlvolume V total blood volume in the aorta V₀ total blood volume in theaorta when the blood pressure is zero w wall thickness of the aorta xaxial position along the aorta δ increased inside diameter of the aortadue to pressurization δC local compliance of the control volume δx axiallength of the control volume ΔP pulse pressure Δt transit time for thepressure wave ΔV stroke volume of the left ventricle ρ blood density vPoisson's ratio

It should be understood that the above-listed terms/variables may notalways be repeated in relation to the symbols used in the disclosureand, thus, the disclosure should be read with reference to thenomenclature provided in Table 1.

I. BLOOD PRESSURE EMBODIMENT

FIG. 1 shows a schematic for a section of the abdominal aorta that isused to conduct a blood pressure analysis in accordance with anembodiment of the invention. In FIG. 1, the symbol Q represents thevolumetric flow-rate of blood from the left ventricle of the heart whichis injected into the aorta during systole. The instantaneous pressureand volume of blood in the aorta are shown by the symbols P and V,respectively. Assuming that the fluid flow through the capillary beds ischaracterized by a low Reynolds number, the perfusion flow exiting theaorta is shown by the quantity P/R where the symbol R is used todescribe the total peripheral resistance of the body. FIG. 1 also showsbasic dimensions for the section of the abdominal aorta, including theoutside diameter D, the inside diameter d, the wall thickness w, and thesection length L.

Using the flow terms that are depicted in FIG. 1, an expression for theconservation of mass may be written as follows:

$\begin{matrix}{0 = {Q - {\frac{1}{R}P} - \frac{dV}{dt}}} & (1)\end{matrix}$

where dV/dt is the time rate-of-change of the blood volume within theaorta.

By definition, the capacitance of any fluid volume is given by thefollowing equation:

$\begin{matrix}{C = \frac{dV}{dP}} & (2)\end{matrix}$

Substituting equation (2) into equation (1) and rearranging termsproduces the following governing equation for the blood pressure withinthe abdominal aorta:

$\begin{matrix}{Q = {{C\frac{dP}{dt}} + {\frac{1}{R}P}}} & (3)\end{matrix}$

If the volumetric flow rate of blood coming from the left ventricle Q ismodeled in a piecewise fashion in order to approximate the blood flowfrom the left ventricle during systole and diastole, the followingexpressions may be obtained:

$\begin{matrix}{{Q = {{\frac{\Delta\; V}{T_{e}}\mspace{14mu}{for}\mspace{20mu} 0} < t < T_{e}}}{Q = {{0\mspace{14mu}{for}\mspace{14mu} T_{e}} < t < T}}} & (4)\end{matrix}$

where ΔV is the stroke volume for the left ventricle during the ejectionperiod T_(e), and T is the heartbeat period.

Substituting equation (3) into equation (4) and conducting a piecewiseintegral, the following expressions may be written to describe theinstantaneous blood pressure within the aorta:

$\begin{matrix}{{P = {{\frac{R\;\Delta\; V}{T_{e}} - {( {\frac{R\;\Delta\; V}{T_{e}} - P_{d}} ){{Exp}( {{- \frac{1}{RC}}t} )}\mspace{14mu}{for}\mspace{14mu} 0}} < t < T_{e}}}{P = {{P_{s}\;{{Exp}( {{- \frac{1}{RC}}( {t - T_{e}} )} )}\mspace{14mu}{for}\mspace{14mu} T_{e}} < t < T}}} & (5)\end{matrix}$

Equation (5) may be evaluated when t=T_(e) and t=T to write thefollowing expressions for systolic pressure P_(s) and diastolic pressureP_(d):

$\begin{matrix}{P_{s} = {\frac{R\;\Delta\; V}{T_{e}}\frac{1 - {{Exp}( {{- \frac{1}{RC}}T_{e}} )}}{1 - {{Exp}( {{- \frac{1}{RC}}T} )}}}} & (6) \\{P_{d} = {\frac{R\;\Delta\; V}{T_{e}}\frac{1 - {{Exp}( {\frac{1}{RC}T_{e}} )}}{1 - {{Exp}( {\frac{1}{RC}T} )}}}} & (7)\end{matrix}$

Systolic and diastolic pressures are known health markers forhypertensive patients, and equations (6) and (7) show that thesepressures are determined by five parameters: total cardiovascularcapacitance C, total peripheral resistance R, left-ventricle strokevolume ΔV, heartbeat period T, and ejection period T_(e).

The mean arterial pressure P_(m) may be determined by taking theintegral average of the solution to equation (3) over the duration of asingle heartbeat, which may be expressed as follows:

$\begin{matrix}{P_{m} = {{\frac{1}{T}{\int_{0}^{T}{Pdt}}} = {{P_{d}\frac{T_{e}}{T}\frac{1 - ( {P_{s}\text{/}P_{d}} )^{\frac{T}{T - T_{e}}}}{1 - ( {P_{s}\text{/}P_{d}} )^{\frac{Te}{T - T_{e}}}}} = \frac{R\;\Delta\; V}{T}}}} & (8)\end{matrix}$

where ΔV/T is the cardiac output. Equation (8) shows that the meanarterial pressure is equal to the cardiac output ΔV/T multiplied by thetotal peripheral resistance R.

A simplified form of equation (8) may be written for a healthy ejectionperiod equal to one-third of the heartbeat period. SubstitutingT_(e)=T/3 into equation (8), the mean arterial pressure P_(m) may beexpressed as follows:

$\begin{matrix}{P_{m} = \frac{P_{s} + P_{d} + \sqrt{P_{s}P_{d}}}{3}} & (9)\end{matrix}$

Equation (9) may be used to obtain an approximation for the meanarterial pressure when the ejection period is unknown.

It should be noted that equation (9) predicts a slightly higher meanarterial pressure compared to the “33% formula” commonly used in theclinic and given by P_(m)=P_(d)+(P_(s)−P_(d))/3. This difference is dueto the rectangular flow model in equation (4). Thus, for a healthy bloodpressure of P_(s)=120 mm-Hg and Pd=80 mm-Hg, it may be shown that themean arterial pressure calculated using equation (9) is 6.4% higher thanthe mean arterial pressure calculated using the “33% formula.”

The pulse pressure ΔP is defined as the difference between the systolicand diastolic pressures (which may be calculated from equations (6) and(7), respectively), as follows:

ΔP=P _(s) −P _(d)  (10)

The pulse pressure is often used to provide a qualitative assessment foraortic compliance. A large pulse pressure is considered an indicator forlow compliance and high aortic stiffness.

The aortic compliance C and peripheral resistance R may be separatelydetermined using the systolic and diastolic pressures (which may becalculated from equations (6) and (7), respectively) and the meanarterial pressure (which may be calculated from equation (8)), asfollows:

$\begin{matrix}{C = {{\frac{\Delta\; V}{P_{m}}\frac{T - T_{e}}{T}\frac{1}{\ln( {P_{s}\text{/}P_{d}} )}} = {\frac{\Delta\; V}{P_{d}}\frac{T - T_{e}}{T}\frac{1}{1{n( {P_{s}\text{/}P_{d}} )}}\frac{1 - ( {P_{s}\text{/}P_{d}} )^{\frac{T_{e}}{T - T_{e}}}}{1 - ( {P_{s}\text{/}P_{d}} )^{\frac{T}{T - T_{e}}}}}}} & (11) \\{\mspace{79mu}{R = {\frac{P_{m}T}{\Delta\; V} = {\frac{P_{d}T_{e}}{\Delta\; V}\frac{1 - ( {P_{s}\text{/}\; P_{d}} )^{\frac{T}{T - T_{e}}}}{1 - ( {P_{s}\text{/}P_{d}} )^{\frac{T_{e}}{T - T_{e}}}}}}}} & (12)\end{matrix}$

With reference to equations (11) and (12), it is important to note thatthe aortic compliance C and peripheral resistance R may be determinedwith knowledge of five parameters: stroke volume ΔV, ejection periodT_(e), heartbeat period T, diastolic pressure P_(d), and systolicpressure P_(s). Three of these parameters—heartbeat period T, diastolicpressure P_(d), and systolic pressure P_(s)—are routinely measured in adoctor's office. The other two parameters—stroke volume ΔV and ejectionperiod T_(e)—may be measured from echocardiogram data. Thus, all fiveparameters are available from a fully exploited echocardiogramexamination in a hospital, clinic or other healthcare setting. Equation(11) also shows that the aortic compliance C manifests itself as ahighly nonlinear combination of these five parameters.

As an example, for a patient with a resting heart rate of 70 bpm, anejection period of 0.286 seconds, a stroke volume of 70 mL, and systolicand diastolic pressures of 120 mm-Hg over 80 mm-Hg, respectively, it maybe calculated from equation (9) that the patient has a healthy aorticcompliance of 1.159 mL/mm-Hg. For the same individual, it may becalculated from equation (10) that the patient has a healthy peripheralresistance of 1.216 mm-Hg-s/mL.

As noted above, equation (9) is a simplified form of equation (8) thatmay be used in cases where a healthy ejection period is equal toone-third of the heartbeat period. Substituting T_(e)=T/3 into equations(11) and (12), the aortic compliance C and peripheral resistance R maybe written as follows:

$\begin{matrix}{C = {\frac{\Delta\; V}{P_{s} + P_{d} + \sqrt{P_{s}P_{d}}}\frac{2}{\ln( {P_{s}\text{/}P_{d}} )}}} & (13) \\{R = {\frac{P_{s} + P_{d} + \sqrt{P_{s}P_{d}}}{3}\frac{T}{\Delta\; V}}} & (14)\end{matrix}$

Equations (13) and (14) may be used to estimate the aortic compliance Cand peripheral resistance R when the ejection period T_(e) is unknown.It can be appreciated that an estimate for the stroke volume ΔV willalso be needed for these calculations. In one embodiment, the strokevolume ΔV is estimated based on a person's age, height, medical history,weight, and/or previous measurements.

As shown in equation (2), the aortic compliance C for the section of theabdominal aorta shown in FIG. 1 is given by the derivative of the bloodvolume V with respect to the blood pressure P. Using the geometry ofFIG. 1, the blood volume of the aortic section is given by the followingequation:

$\begin{matrix}{V = {\frac{\pi}{4}d^{2}L}} & (15)\end{matrix}$

As the aorta is pressurized, the inside diameter d increases as follows:

d=d ₀+δ  (16)

where d₀ is the inside diameter of the aorta when the blood pressure iszero, and δ is the increased diameter due to pressurization of thevessel.

It is known that the increased diameter for a thick-wall pressure vesselwithout capped ends is given by the following equation:

$\begin{matrix}{\delta = {d_{0}\frac{P}{E}( {\frac{D_{0}^{2} + d_{0}^{2}}{D_{0}^{2} - d_{0}^{2}} + v} )}} & (17)\end{matrix}$

It should be noted that thick-wall pressure vessel calculations are alsovalid for thin-wall pressure vessels. In equation (17), P is the fluidpressure within the vessel, E is the modulus of elasticity for thevessel material, v is Poisson's ratio for the vessel material, and D, isthe outside diameter of the pressure vessel when the pressure is zero.By substituting equations (15) and (16) into equation (17) and takingthe derivative of the volume with respect to pressure, the followingexpression may be written to describe the aortic compliance of theaortic section shown in FIG. 1:

$\begin{matrix}{C = {\frac{\pi\;{Ld}_{0}^{2}}{2\; E}( {\frac{D_{0}^{2} + d_{0}^{2}}{D_{0}^{2} - d_{0}^{2}} + v} )}} & (18)\end{matrix}$

In equation (18), the pressure-dependence of the aortic compliance hasbeen neglected due to its small size.

II. PULSE-WAVE VELOCITY (PWV) EMBODIMENT

FIG. 2 shows a schematic for an infinitesimal control volume within asegment of an aorta that is used to conduct a pulse-wave velocity (PWV)analysis in accordance with an embodiment of the invention. The dashedline indicates the control volume that has a length shown by the symbolδx. The local pressure and blood velocity within the aorta are given bythe symbols P and u, respectively. The local cross-sectional area of theaorta is shown by the symbol A and the total length of the aorta segmentis given by the symbol L. The aorta is a type of a hydraulictransmission line where the pressure varies as a function of time t andlocation in the longitudinal direction x. The wave equation for thepressure within the transmission line is known to exist in the followingform:

$\begin{matrix}{\frac{\partial^{2}P}{\partial t^{2}} = {c^{2}\frac{\partial^{2}P}{\partial x^{2}}}} & (19)\end{matrix}$

where c is the propagation speed of the pressure wave within the aorta,which is also known as the pulse-wave velocity (PWV). As describedbelow, it is possible to derive an expression for PMV as a function ofphysically relevant parameters.

In the analysis described below, the following assumptions are made: (1)the blood will be considered incompressible, while the aorta will beconsidered elastic; (2) the inflow of momentum across the control volumeboundary is negligible compared to the time rate-of-change of momentumwithin the control volume, and will thus be neglected; (3) the viscousshear stress at the inside wall of the aorta will be neglected; (4) theblood pressure varies with time t and in the longitudinal x-direction,but not in the radial direction; (5) the cross-sectional area of theaorta varies with time and in the longitudinal x-direction due to theelasticity of the vessel and the local pressure; and (6) quadraticallysmall terms throughout the analysis will be neglected.

Using the Reynolds transport theorem, the conservation of mass for thecontrol volume shown in FIG. 1 is given by the following equation:

$\begin{matrix}{0 = {{\frac{\partial}{\partial t}{\int_{cv}{\rho\;{dv}}}} + {\int_{cs}{{p( {u \cdot \hat{n}} )}{da}}}}} & (20)\end{matrix}$

where ρ is the fluid density, dv is an infinitesimally small volume offluid, u is the blood velocity vector, and if is a unit vector thatpoints normally outward from the control surface across which blood ispassing. The first term on the right-hand side of equation (20)represents the time rate-of-change of mass within the control volume,and the second term on the right-hand side of equation (20) representsthe inflow of mass across the control volume boundary.

If the blood is treated as an incompressible fluid, the fluid density inequation (20) may be canceled from the expression resulting in thefollowing equation for the conservation of mass:

$\begin{matrix}{0 = {{\frac{\partial}{\partial t}{\int_{cv}{dv}}} + {\int_{cs}{( {u \cdot \hat{n}} ){da}}}}} & (21)\end{matrix}$

The first term on the right-hand side of equation (21) may be expressedas follows:

$\begin{matrix}{{\frac{\partial}{\partial t}{\int_{cv}{dv}}} = {{\frac{\partial}{\partial t}( {\overset{\_}{A}\;\delta\; x} )} = {\frac{\partial A}{\partial t}\delta x}}} & (22)\end{matrix}$

When the quadratically small terms in equation (22) are neglected, theaverage cross-sectional area of the control volume may be expressed asfollows:

$\begin{matrix}{\overset{¯}{A} = {\frac{1}{2}( {A + A + {\frac{\partial A}{\partial x}\delta x}} )}} & (23)\end{matrix}$

The second term on the right-hand side of equation (21) may be expressedas follows:

$\begin{matrix}\begin{matrix}{{\int_{cs}{( {u \cdot \hat{n}} ){da}}} = {{- {uA}} + {( {u + {\frac{\partial u}{\partial x}\delta x}} )( {A + {\frac{\partial A}{\partial x}\delta x}} )}}} \\{= {{- {uA}} + {uA} + {A\frac{\partial u}{\partial x}\delta x} + {u\frac{\partial A}{\partial x}\delta x} + {\frac{\partial u}{\partial x}\frac{\partial A}{\partial x}\;\delta\; x^{2}}}}\end{matrix} & (24)\end{matrix}$

Neglecting quadratically small terms, equation (24) may be simplified asfollows:

$\begin{matrix}{{\int_{cs}{( {u \cdot \hat{n}} ){da}}} = {{\frac{\partial( {Au} )}{\partial x}\delta x} = {\frac{\partial Q}{\partial x}\delta x}}} & (25)\end{matrix}$

where A times u is equal to the volumetric flow rate Q.

Substituting equations (22) and (25) into equation (21) produces thefollowing expression for the conservation of mass:

$\begin{matrix}{0 = {\frac{\partial A}{\partial t} + \frac{\partial Q}{\partial x}}} & (26)\end{matrix}$

where the axial length of the control volume δx has canceled out. Itwill be seen that equation (26) will be used to develop thepressure-wave equation for the aorta.

Using the Reynolds transport theorem, the conservation of momentum forthe control volume shown in FIG. 1 is given by the following equation:

$\begin{matrix}{\frac{Dp}{Dt} = {{\frac{\partial}{\partial t}{\int_{cv}{\rho udv}}} + {\int_{cs}{{{\rho u}( {u \cdot \hat{n}} )}{da}}}}} & (27)\end{matrix}$

where Dp/Dt is the material derivative of the fluid momentum vector p.The first term on the right-hand side of equation (27) represents thetime rate-of-change of momentum within the control volume, and thesecond term on the right-hand side of equation (27) represents theinflow of momentum across the control volume boundary.

With respect to the blood-pressure problem within the aorta, dimensionalanalysis may be used to show that the inflow of momentum across thecontrol volume boundary is at least one order of magnitude smaller thanthe time rate-of-change of momentum within the control volume. For thisreason, the second term on the right-hand side of equation (27) will beneglected and the conservation of momentum will be written as follows:

$\begin{matrix}{\frac{Dp}{Dt} = {\frac{\partial}{\partial t}{\int_{cv}{\rho udv}}}} & (28)\end{matrix}$

According to Newton's second law, the time rate-of-change for the fluidmoment must be equal to the forces that are acting on the surfaces ofthe control volume. If we neglect shear stress at the inside wall of theaorta and only consider the pressures acting to push the control volumein the positive x-direction, the left-hand side of equation (28) may bewritten as follows:

$\begin{matrix}\begin{matrix}{\frac{Dp}{Dt} = {{PA} - {( {P + {\frac{\partial P}{\partial x}\delta x}} )( {A + {\frac{\partial A}{\partial x}\delta x}} )}}} \\{= {{PA} - {PA} - {A\frac{\partial P}{\partial x}\delta x} - {P\frac{\partial A}{\partial x}\delta x} - {\frac{\partial P}{\partial x}\frac{{\partial A}\;}{\partial x}\delta\; x^{2}}}}\end{matrix} & (29)\end{matrix}$

Neglecting quadratically small terms produces the following result forthe time rate-of-change for the fluid momentum within the aorta:

$\begin{matrix}{\frac{Dp}{Dt} = {{- \frac{\partial( {PA} )}{\partial x}}\delta x}} & (30)\end{matrix}$

where the vector direction of this result is in the positivex-direction.

It should be noted that previous developments for the PWV equation treatthe cross-sectional area A as a constant rather than considering thisparameter to vary with respect to x. This is inconsistent with theconservation-of-mass equation presented in equation (26). If thecross-sectional area A is assumed to be independent of x, the final PWVresult will be independent of pressure and a significant physicalcontributor will be lost.

If the fluid density is considered to be constant, and the fluidvelocity within the control volume is assumed to be uniform and averagein the positive x-direction, the time rate-of-change of the fluidmomentum within the control volume may be written as follows:

$\begin{matrix}{{\frac{\partial}{\partial t}{\int_{cv}{\rho udv}}} = {{\frac{\partial}{\partial t}( {\overset{\_}{u}{\int_{cv}{dv}}} )} = {{\rho\frac{\partial}{\partial t}( {\overset{\_}{u}\overset{¯}{A}\delta x} )} = {\rho\frac{\partial Q}{\partial t}\delta x}}}} & (31)\end{matrix}$

where the average velocity of the fluid within the control volume isgiven by the following equation:

$\begin{matrix}{\overset{\_}{u} = {\frac{1}{2}( {u + u + {\frac{\partial u}{\partial x}\delta x}} )}} & (32)\end{matrix}$

and where the average cross-sectional area of the control volume Ā isgiven in equation (23). It should be noted that quadratically smallterms have been neglected in equation (31).

Substituting equations (30) and (31) into equation (28) produces thefollowing expression for the conservation of momentum:

$\begin{matrix}{0 = {\frac{\partial Q}{\partial t} + {\frac{1}{\rho}\frac{\partial( {PA} )}{\partial x}}}} & (33)\end{matrix}$

where, again, the axial length of the control volume δx has canceled.This form of the conservation of momentum will be used to develop thepressure-wave equation for the aorta.

Equations (26) and (33) represent the conservation of mass and momentum,respectively, for the blood flowing through the aorta shown in FIG. 1.Taking the derivative of the conservation of mass with respect to time,and the derivative of the conservation of momentum with respect to thespatial coordinate x, the following equations may be written:

$\begin{matrix}{{\frac{\partial}{\partial t}( \frac{\partial Q}{\partial x} )} = {{{\frac{\partial^{2}A}{\partial t^{2}}\mspace{14mu}{and}}\mspace{14mu} - {\frac{\partial}{\partial x}( \frac{\partial Q}{\partial t} )}} = {\frac{1}{\rho}\frac{\partial^{2}( {PA} )}{\partial x^{2}}}}} & (34)\end{matrix}$

Because differentiation is a linear operator, we recognize that:

$\begin{matrix}{{\frac{\partial}{\partial t}( \frac{\partial Q}{\partial x} )} = {\frac{\partial}{\partial x}( \frac{\partial Q}{\partial t} )}} & (35)\end{matrix}$

Using equations (34) and (35), the wave equation for the blood flowproblem may be written as follows:

$\begin{matrix}{{\rho\frac{\partial^{2}A}{\partial t^{2}}} = \frac{\partial^{2}( {PA} )}{\partial x^{2}}} & (36)\end{matrix}$

This is the basic form of the wave equation that will be furtherdeveloped below using a constitutive model for the cross-sectional areaA as a function of blood pressure P.

Equation (36) shows that the wave equation is dependent upon the localcross-sectional area A. Using the definition for volumetric compliance,it may be shown that this area is given by the following equation:

$\begin{matrix}{A = {A_{o} + {\frac{\delta C}{\delta x}P}}} & (37)\end{matrix}$

where A_(o) is the local cross-sectional area when the pressure is zero,δC is the local compliance, and δx is the length of the local controlvolume shown in FIG. 1. By substituting equation (37) into equation (36)and neglecting small terms, the wave equation may be written as follows:

$\begin{matrix}{\frac{\partial^{2}P}{\partial t^{2}} = {{c^{2}\frac{\partial^{2}P}{\partial x^{2}}\mspace{14mu}{where}\mspace{14mu} c^{2}} = {\frac{1}{\rho}( {{A_{o}\frac{\delta x}{\delta C}} + {2P}} )}}} & (38)\end{matrix}$

In equation (38), c is the propagation speed of the pressure wave withinthe aorta, which is also equal to the PWV.

The wave equation presented in equation (38) has been developed todescribe the blood pressure at a specific time and location within theaorta. By rearranging terms in equation (38), the local compliancewithin the aorta may be expressed as follows:

$\begin{matrix}{{\delta C} = {\frac{A_{o}}{{\rho c^{2}} - {2P}}\delta x}} & (39)\end{matrix}$

Using this form, we may consider the average or overall compliance ofthe aorta to be the following:

$\begin{matrix}{C = \frac{V_{o}}{{\rho PWV^{2}} - {2P_{m}}}} & (40)\end{matrix}$

where V_(o) is the volume of blood in the aorta when the pressure iszero, P_(m) is the mean arterial pressure, and PWV is the pulse-wavevelocity of the blood as measured by known methods for obtaining thecarotid-femoral PWV measurement, as described in the Background sectionabove. A significant difference exists between equation (40) andprevious known expressions, i.e., equation (40) contains a pressure termthat has not been included in previous results. This applied pressure tothe fluid is dimensionally significant if 2 P_(m)/(ρPWV²) is greaterthan 1/10 as demonstrated herein.

For a typical adult, the cardiovascular system has about 5 liters ofblood and 7% of this blood is contained in the aorta. This means thatthe nominal blood volume in the aorta is 350 milliliters. The density ofblood is 1060 kilograms/meter³ (slightly more than water) and a healthymean arterial pressure is 100 mm-Hg. Furthermore, a healthy PWV is givenby 8 meters/second. Using these parameters with equation (40), it may beshown that a healthy aortic compliance is given by 1.133 mL/mm-Hg, whichis similar to the healthy compliance that was calculated using theblood-pressure model presented in equation (11). If the mean arterialpressure is neglected in equation (40), the aortic compliance will becalculated as 0.688 ml/mm-Hg, which is 39% lower than the expectedcompliance. Thus, the pressure dependency of equation (40) is importantand provides a more accurate result than previous known expressions.

III. IN VITRO EXPERIMENTS

FIG. 3 shows a schematic for an experimental setup that was used toperform in vitro experiments in relation to the blood pressure and PWVembodiments of the invention. In this setup, the left ventricle of theheart is simulated by a pulsatile pump available from BDC Laboratoriesof Wheat Ridge, Colo. This pump is actuated electromagnetically with anability to deliver a programed flow-pulse that is characterized by aspecific stroke volume ΔV, heartbeat period T, and ejection period Te.The aortic valve and the mitral valve are simulated by check valves,which allow flow in only one direction as shown by the symbols q_(a) andq_(m), respectively. The aorta model is shown in FIG. 3 as a straighttube of length L and a nominal cross-sectional area given by A. Thevolume of fluid within the aorta is shown by V. A needle valve is usedto adjust the mean arterial pressure within the aorta, and the flow rateacross this valve is assumed to be of the low Reynolds-number type,being proportional to the pressure drop across the valve P and inverselyproportional to the valve resistance R. The valve resistance R mimicsthe peripheral resistance of the human body. The low-pressure reservoiris used to simulate the venous side of the cardiovascular system. Theworking fluid in the experiments is water, not a blood-mimicking fluid.In order to measure the PWV, pressure transducers are located in thevicinity of the two ends of the aorta, identified by the symbols P₁ atthe top of the tube and P₂ at the bottom of the tube. The pressuretransducers are capable of measuring pressures between −362 and 3878mm-Hg with an accuracy better than ±2% of reading. The pressuretransducers have a frequency response of 1.2 kHz.

The in vitro experiments performed using the setup shown in FIG. 3 usedtwo model aortae. The first aorta was an elastic tube made from siliconerubber, with an inside diameter of 2.54 cm and a wall thickness of 1.4mm. The length of the tube was 36.5 cm, making the unpressurized volumeof fluid in the aorta equal to 185 mL. The modulus of elasticity for thesilicone rubber was approximately 1.3 MPa. The second aorta was anactual aorta harvested from a 1 year-old Holstein heifer. This aorta was51 cm in length and had an inside diameter that transitioned linearlyfrom 2.9 cm to 1.1 cm. The unpressurized volume of the aorta was 175 mL.

The experiments were designed to capture data that would be used for twopurposes: (1) to compare the compliance results of equation (11) (fromthe blood pressure embodiment) and equation (40) (from the PWVembodiment); and (2) to demonstrate the dependency of these results onthe mean arterial pressure. In order to conduct these experiments, thestroke volume of the pulsatile pump A V was set to 50 mL for the rubbertube and 70 mL for the Holstein aorta, the heartbeat period T was set to1 second, and the ejection period T_(e) was set to ⅓ second. Sixteendifferent needle-valve settings were used to create a range of meanpressures in the aorta between 50 and 200 mm-Hg. Each needle-valvesetting corresponded to an increase in the mean arterial pressure ofapproximately 10 mm-Hg. Three seconds of data were taken for eachexperiment at a sample rate of 5 kHz.

During the experiments, the systolic and diastolic pressures in theaorta were identified and the mean arterial pressure was calculatedusing equation (8). Using these blood-pressure measurements with theknown flow parameters of the pulsatile pump, the compliance of the aortawas calculated using equation (11). Similarly, the pressures P₁ and P₂were taken and compared to determine the transit time Δt between the twopressure-wave forms. The method used to calculate the transit time isknown as the tangent-intersection, foot-to-foot method and isrecommended for most PWV transit time measurements. Once the transittime was determined, the PWV was calculated using the standard method(PWV=L/Δt) and the compliance of the aorta was calculated using equation(40).

FIGS. 4 and 5 are plots showing the compliance and PWV results versusthe mean arterial pressure for the elastic tube and the Holstein aorta,respectively. The scales for these two plots are identical in order tofacilitate a visual comparison between them.

First, it can be observed from FIGS. 4 and 5 that the compliance resultscomputed using equations (11) and (40), respectively, are similar inboth magnitude and shape. The average percent difference between the twocalculations is less than 7%. This agreement suggests that both methodsmay be used to compute the aortic compliance depending upon theavailable data. It is also shown in FIGS. 4 and 5 that the elastic tubewas generally less compliant than the Holstein aorta. This differencewas due to material and geometric properties of the aortae.

Second, it can be observed from FIGS. 4 and 5 that the elastic tube andthe Holstein aorta present a compliance that is dependent upon the meanarterial pressure. In previous research where the aortic compliance hasbeen described as a function of PWV, this dependence has been neglected;however, FIGS. 4 and 5 show that the mean arterial pressure must beconsidered when determining compliance.

Third, it can be observed from FIGS. 4 and 5 that the compliance of therubber material increases throughout the pressure range studied in thisresearch, and the compliance of the biological material decreases afterthe mean pressure exceeds 100 mm-Hg. A physical explanation for thedifference in behavior is undoubtedly due to different materialproperties for the aortae. For example, mechanical testing has shownthat the modulus of elasticity of silicon-rubber decreases slightly withstrain, while the modulus of elasticity of a porcine aorta increasessignificantly with strain.

Of course, it should be understood that the results of the in vitroexperiments described above do not have a one-to-one correspondence withthe in vivo compliance that may be expected from an animal or humanbeing. The surrounding tissues of the body and extended blood vesselswill undoubtedly affect the total compliance of the cardiovascularsystem.

IV. CLINICAL IMPLICATIONS AND COMPUTING SYSTEM

One clinical implication of the invention is that equations (11) and(12) may be used to noninvasively determine the aortic compliance andperipheral resistance of a patient if the following data is known: thediastolic pressure, the systolic pressure, the heartbeat period, thestroke volume, and the ejection period of the patient. Blood pressure isroutinely measured in the clinic to determine the systolic and diastolicpressures of the blood-pressure pulse. Any suitable device may be usedto measure blood pressure, such as mercury sphygmomanometers, aneroidsphygmomanometers, and digital meters. The heartbeat period (i.e., heartrate) is also routinely measured in the clinic, either manually or usingany suitable heart rate monitor. The stroke volume and ejection periodmay be determined from echocardiogram data in order to obtain accuratenumbers for a specific patient. Because an echocardiogram is more commonand easier to perform than a PWV test, and since insurance companiestypically pay for echocardiograms, this clinical implementation maybecome a standard clinical practice (possibly displacing the need forthe PWV test altogether) and will provide important information that iscurrently not available to the physician. It is believed that access tosuch information will improve the prescribed treatment for patients withcardiovascular disease.

Alternatively, equations (13) and (14) may be used to noninvasivelydetermine the aortic compliance and peripheral resistance of a patientif the following data is known: the diastolic pressure, the systolicpressure, the heartbeat period, the an estimated stroke volume. Thisalternative may be used when an echocardiogram is not performed and,thus, the ejection period of the patient is not known. The stroke volumemay be estimated, for example, based on based on a person's age, height,medical history, weight, and/or previous measurements.

Another clinical implication of the invention is that equation (40) maybe used to noninvasively determine the aortic compliance of a patientbased on the PWV and mean arterial pressure (noting that the meanarterial pressure is not typically considered in connection with aconventional PWV test). The PWV may be measured using known methods forobtaining the carotid-femoral PWV measurement. The mean arterialpressure may be determined using equation (8) if the following fourparameters are known—diastolic pressure, systolic pressure, heartbeatperiod, and ejection period (which may be obtained in the same manner asdescribed above). Alternatively, the mean arterial pressure may beestimated using equation (9) if only the diastolic and systolicpressures are known.

Each of the above methods may be implemented using a softwareapplication executed on a computing device by performing the followingsteps: receiving the relevant parameters and/or test results (which willvary depending on which method is used); determining the aorticcompliance and/or peripheral resistance based on the received data; andpresenting the aortic compliance and/or peripheral resistance via a userinterface to enable a physician or other clinician to identify acardiovascular disease of the patient. One skilled in the art willappreciate that a number of different system configurations may be used,including a system in which the software application is executed locallyon a computer located at a clinic, or, a system in which the softwareapplication is executed on a server in communication with one or moreclient computers located at a clinic. The latter system may be used, forexample, when the software application is implemented as part of ahealth record system that maintains electronic medical records (EMRs)for patients.

Referring to FIG. 6, an exemplary embodiment of a health record systemis shown generally as reference numeral 600. The system 600 includes aserver 602 in communication with a plurality of client computers(wherein only one client computer 604 is shown) via a communicationsnetwork 638. Each of the client computers may comprise a computerworkstation, a personal computer, a laptop computer, a personalcomputing tablet, a smartphone, or any other electronic computing deviceknown in the art. In general, each client computer is utilized by a userof system 600 and, accordingly, system 600 may include hundreds or eventhousands of client computers.

The communications network 638 may comprise any network capable offacilitating the exchange of data between the server 602 and each clientcomputer 604, such as those that operate according to the IEEE 802.3protocol (e.g., Ethernet) or the IEEE 802.11 protocol (e.g., Wi-Fi). Forexample, in some embodiments, the communications network 638 comprises alocal area network (LAN), wireless LAN (WLAN), wide area network (WAN),and/or wireless WAN (WWAN), which is connectable to other communicationsnetworks and/or portions of the Internet or an intranet. Thecommunications infrastructure may comprise any medium that allows datato be physically transferred through serial or parallel communicationchannels (e.g., Ethernet cable, wireless communication channels,cellular communications, optical fiber, copper wire, etc.).

As shown in FIG. 6, the server 602 generally includes a processor 606, amemory 608, a storage device 614, a network interface 618, an inputdevice 620, and an output device 622, all of which are connected via anysuitable bus arrangement. The processor 606 may comprise a singlecentral processing unit (CPU), multiple CPUs, a single CPU havingmultiple processing cores, and the like. The memory 608 may be a randomaccess memory (RAM), for example, although other types of memory may beused. The memory stores the operating system 610 for server 602, as wellas a software application 612 (described below). The storage device 614may comprise any type of fixed and/or removable storage device suitablefor storing a database containing a plurality of electronic medicalrecords (EMRs). Two EMRs are shown in FIG. 6—an EMR for patient A 616 aand an EMR for patient B 616 b—although a large number of EMRs wouldtypically be stored in storage device 614. The network interface 618 maybe any type of network interface that allows the server 602 tocommunicate with other computers via the communications network 638. Theinput device 620 may be any device capable of providing input to theserver 602, such as a keyboard and/or a mouse. The output device 622 maybe any device capable of providing output to a user of the server 602,such as any conventional display screen.

Software application 612 is programmed to determine the aorticcompliance and/or peripheral resistance of a patient by implementing anyof the methods described herein. In this embodiment, the softwareapplication 612 comprises instructions that, when executed by theprocessor 606, cause the processor 606 to: (i) access an electronicmedical record (e.g., one of EMRs 616 a and 616 b) to retrieve therequired patient data (e.g., one or more of the diastolic pressure, thesystolic pressure, the heartbeat period, the stroke volume, and theejection period for the patient); (ii) determine the aortic complianceand/or peripheral resistance for the patient based on the retrievedpatient data; and (iii) cause the aortic compliance and/or peripheralresistance to be presented on output device 636 of client computer 604to enable identification of a cardiovascular disease of the patient.

Each client computer 604 contains a processor 624, a memory 626 (withoperating system 628), a storage device 630, a network interface 632, aninput device 634, and an output device 636. The description andfunctionality of these components is generally the same as thecorresponding components described above in reference to server 602. Itshould be understood that the input device 634 enables a user to inputpatient data that is stored within a patient's EMR, i.e., the inputtedpatient data is transmitted from the client computer 604 to the server602 for storage within the appropriate EMR of storage device 614. Forexample, the inputted data may comprise the diastolic pressure, thesystolic pressure, the heartbeat period, the stroke volume, and/or theejection period for the patient. Also, the output device 636 presentsthe aortic compliance and/or peripheral resistance to thereby enable aphysician or other clinician to identify a cardiovascular disease of apatient. For example, the processor 606 of server 602 executes thesoftware application 612 to determine the aortic compliance and/orperipheral resistance, as described above, and such information istransmitted from the server 602 to the client computer 604 for displayon the output device 636.

It should be understood that the system 600 shown in FIG. 6 is anexemplary embodiment and that other system configurations may be used toimplement the invention. For example, although system 600 includes asingle server 102, any number of servers may be used for providing thefunctionality described herein. Also, while system 600 includes a singlestorage device 614 for storing patient data, the patient data mayalternatively be stored in different storage devices residing on thesame or different servers. For example, all or a portion of the patientdata may be stored on a remote file server that is accessed through thecommunications network 638.

V. CONCLUSIONS

As described above, aortic compliance is known to be an independentpredictor of cardiovascular morbidity and mortality. Assuming that thehuman aorta behaves similar to that of the Holstein heifer used in theexperiments described above, it can be shown that aortic stiffeningaccompanies hypertension as the mean arterial blood pressure increases.This is due to the elastic properties of the biological material that isdifferent from the silicone-rubber material used in the experiments.Thus, the following conclusions are supported by this disclosure:

(1) The aortic compliance computed from the blood pressure model(equation 11) and the PWV model (equation (40)) produce similar results,which suggests that either model may be used to compute aorticcompliance based upon the available data.

(2) If a patient is able to receive echocardiograms, equation (11) maybe used to regularly assess the total cardiovascular compliance forpatients with cardiovascular disease.

(3) The aortic compliance is dependent upon the mean arterial pressurefor both the rubber tube and the Holstein aorta, as shown in FIGS. 4 and5. This pressure dependency has been neglected in previous models thathave sought to relate PWV to aortic compliance. The correct PWV model ispresented in equation (40).

(4) The differences in material properties between the rubber tube andthe Holstein aorta produce different behaviors for the aortic complianceas a function of mean arterial pressure. For the rubber tube, the aorticcompliance increases throughout the entire pressure range as the meanarterial pressure increases. For the Holstein aorta, the aorticcompliance remains constant until the mean arterial pressure exceeds 100mm-Hg. For pressures greater than 100 mm-Hg, the compliance of theHolstein aorta decreases markedly. This difference is due to thedifference in the material properties of each aorta.

Of course, other conclusions will be readily apparent to one skilled inthe art from the disclosure provided herein, or may be learned from thepractice of the invention.

While the present invention has been described and illustratedhereinabove with reference to various exemplary embodiments, it shouldbe understood that various modifications could be made to theseembodiments without departing from the scope of the invention.Therefore, the present invention is not to be limited to the specificsystems or methodologies of the exemplary embodiments, except insofar assuch limitations are included in the following claims.

What is claimed and desired to be secured by Letters Patent is asfollows:
 1. A method for identifying a cardiovascular disease of apatient, comprising: obtaining a first measurement comprising adiastolic pressure for the patient; obtaining a second measurementcomprising a systolic pressure for the patient; obtaining a thirdmeasurement comprising a heartbeat period for the patient; obtaining afourth measurement comprising a stroke volume for the patient; obtaininga fifth measurement comprising an ejection period for the patient; anddetermining an aortic compliance for the patient based on the diastolicpressure, the systolic pressure, the heartbeat period, the strokevolume, and the ejection period.
 2. The method of claim 1, wherein thediastolic pressure, the systolic pressure, and the heartbeat period areeach measured directly from the patient.
 3. The method of claim 1,further comprising obtaining echocardiogram data for the patient,wherein the stroke volume and the ejection period are each measured fromthe echocardiogram data.
 4. The method of claim 1, wherein the aorticcompliance is determined based on the following equation:$C = {\frac{\Delta\; V}{P_{d}}\frac{T - T_{e}}{T}\frac{1}{\ln\;( {P_{s}/P_{d}} )}\frac{1 - ( {P_{s}/P_{d}} )^{\frac{T_{e}}{T - T_{e}}}}{1 - ( {P_{s}/P_{d}} )^{\frac{T_{e}}{T - T_{e}}}}}$where P_(d) is the diastolic pressure, P_(s) is the systolic pressure, Tis the heartbeat period, ΔV is the stroke volume, and T_(e) is theejection period.
 5. The method of claim 1, further comprisingdetermining a peripheral resistance for the patient based on thediastolic pressure, the systolic pressure, the heartbeat period, thestroke volume, and the ejection period.
 6. The method of claim 5,wherein the peripheral resistance is determined based on the followingequation:$R = {\frac{P_{d}T_{e}}{\Delta\; V}\frac{1 - ( {P_{s}/P_{d}} )^{\frac{T}{T - T_{e}}}}{1 - ( {P_{s}/P_{d}} )^{\frac{T_{e}}{T - T_{e}}}}}$where P_(d) is the diastolic pressure, P_(s) is the systolic pressure, Tis the heartbeat period, ΔV is the stroke volume, and T_(e) is theejection period.
 7. A method for identifying a cardiovascular disease ofa patient, comprising: obtaining a first measurement comprising adiastolic pressure for the patient; obtaining a second measurementcomprising a systolic pressure for the patient; obtaining an estimate ofa stroke volume for the patient; and determining an aortic compliancefor the patient based on the diastolic pressure, the systolic pressure,and the stroke volume.
 8. The method of claim 7, further comprising:obtaining one or more of an age, a height, a medical history, a weight,and a previous stroke volume measurement of the patient; determining theestimate of the stroke volume based on the one or more of the age, theheight, the medical history, the weight, and the previous stroke volumemeasurement of the patient.
 9. The method of claim 7, wherein the aorticcompliance is determined based on the following equation:$C = {\frac{\Delta\; V}{P_{s} + P_{d} + \sqrt{P_{s}P_{d}}}\frac{2}{\ln\;( {P_{s}/P_{d}} )}}$where P_(d) is the diastolic pressure, P_(s) is the systolic pressure,and ΔV is the stroke volume.
 10. The method of claim 8, furthercomprising: obtaining a third measurement comprising a heartbeat periodfor the patient; and determining a peripheral resistance for the patientbased on the diastolic pressure, the systolic pressure, the heartbeatperiod, and the stroke volume.
 11. The method of claim 10, wherein theperipheral resistance is determined based on the following equation:$R = {\frac{P_{s} + P_{d} + \sqrt{P_{s}P_{d}}}{3}\frac{T}{\Delta\; V}}$where P_(d) is the diastolic pressure, P_(s) is the systolic pressure, Tis the heartbeat period, and ΔV is the stroke volume.
 12. Anon-transitory computer readable medium storing instructions that, whenexecuted by a processor of a computing device, cause the processor toperform a plurality of operations comprising: accessing an electronicmedical record to retrieve a diastolic pressure, a systolic pressure, aheartbeat period, a stroke volume, and an ejection period associatedwith a patient; determining an aortic compliance for the patient basedon the diastolic pressure, the systolic pressure, the heartbeat period,the stroke volume, and the ejection period; and causing the aorticcompliance to be presented via a user interface to enable identificationof a cardiovascular disease of the patient.
 13. The non-transitorycomputer readable medium of claim 12, wherein the aortic compliance isdetermined based on the following equation:$C = {\frac{\Delta\; V}{P_{d}}\frac{T - T_{e}}{T}\frac{1}{\ln\;( {P_{s}/P_{d}} )}\frac{1 - ( {P_{s}/P_{d}} )^{\frac{T_{e}}{T - T_{e}}}}{1 - ( {P_{s}/P_{d}} )^{\frac{T}{T - T_{e}}}}}$where P_(d) is the diastolic pressure, P_(s) is the systolic pressure, Tis the heartbeat period, ΔV is the stroke volume, and T_(e) is theejection period.
 14. The non-transitory computer readable medium ofclaim 12, wherein the operations further comprise determining aperipheral resistance for the patient based on the diastolic pressure,the systolic pressure, the heartbeat period, the stroke volume, and theejection period.
 15. The non-transitory computer readable medium ofclaim 14, wherein the peripheral resistance is determined based on thefollowing equation:$R = {\frac{P_{d}T_{e}}{\Delta\; V}\frac{1 - ( {P_{s}/P_{d}} )^{\frac{T}{T - T_{e}}}}{1 - ( {P_{s}/P_{d}} )^{\frac{T_{e}}{T - T_{e}}}}}$where P_(d) is the diastolic pressure, P_(s) is the systolic pressure, Tis the heartbeat period, ΔV is the stroke volume, and T_(e) is theejection period.
 16. A non-transitory computer readable medium storinginstructions that, when executed by a processor of a computing device,cause the processor to perform a plurality of operations comprising:receiving a diastolic pressure and a systolic pressure associated with apatient; determining an estimate of a stroke volume associated with thepatient; determining an aortic compliance for the patient based on thediastolic pressure, the systolic pressure, and the stroke volume; andcausing the aortic compliance to be presented via a user interface toenable identification of a cardiovascular disease of the patient. 17.The non-transitory computer readable medium of claim 16, furthercomprising: receiving one or more of an age, a height, a medicalhistory, a weight, and a previous stroke volume measurement of thepatient; determining the estimate of the stroke volume based on the oneor more of the age, the height, the medical history, the weight, and theprevious stroke volume measurement of the patient.
 18. Thenon-transitory computer readable medium of claim 16, wherein the aorticcompliance is determined based on the following equation:${C = \frac{\Delta\; V}{P_{s} + P_{d} + \sqrt{P_{s}P_{d}}}}\frac{2}{\ln\;( {P_{s}/P_{d}} )}$where P_(d) is the diastolic pressure, P_(s) is the systolic pressure,and ΔV is the stroke volume.
 19. The non-transitory computer readablemedium of claim 16, further comprising: receiving a heartbeat periodassociated with the patient; determining a peripheral resistance for thepatient based on the diastolic pressure, the systolic pressure, theheartbeat period, and the stroke volume; and causing the peripheralresistance to be presented via the user interface.
 20. Thenon-transitory computer readable medium of claim 19, wherein theperipheral resistance is determined based on the following equation:$R = {\frac{P_{s} + P_{d} + \sqrt{P_{s}P_{d}}}{3}\frac{T}{\Delta\; V}}$where P_(d) is the diastolic pressure, P_(s) is the systolic pressure, Tis the heartbeat period, and ΔV is the stroke volume.